Rational dynamical systems, S-units, and D-finite power series
文献类型：期刊论文
| 作者 | Bell, Jason P.1; Chen, Shaoshi2; Hossain, Ehsaan3 |
| 刊名 | ALGEBRA & NUMBER THEORY
 |
| 出版日期 | 2021 |
| 卷号 | 15期号:7页码:1699-1728 |
| 关键词 | S-units D-finite series arithmetic dynamics algebraic groups orbits |
| ISSN号 | 1937-0652 |
| DOI | 10.2140/ant.2021.15.1699 |
| 英文摘要 | Let K be an algebraically closed field of characteristic zero, let G be a finitely generated subgroup of the multiplicative group of K, and let X be a quasiprojective variety defined over K. We consider K-valued sequences of the form a(n) = f (theta(n)(x(0))), where theta : X -> X and f : X -> P-1 are rational maps defined over K and x(0) is an element of X is a point whose forward orbit avoids the indeterminacy loci of theta and f. Many classical sequences from number theory and algebraic combinatorics fall under this dynamical framework, and we show that the set of n for which a(n) is an element of G is a finite union of arithmetic progressions along with a set of upper Banach density zero. In addition, we show that if a(n) is an element of G for every n and X is irreducible and the theta orbit of x is Zariski dense in X then there is a multiplicative torus G(m)(d) and maps Psi : G(m)(d) -> G(m)(d) and g : G(m)(d) -> G(m) such that a(n) = (g degrees Psi(n)) (y) for some y is an element of G(m)(d). We then obtain results about the coefficients of D-finite power series using these facts. |
| 资助项目 | NSERC[RGPIN-2016-03632] ; NSFC[11871067] ; NSFC[11688101] ; Fund of the Youth Innovation Promotion Association, CAS ; National Key Research and Development Project[2020YFA0712300] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000715749900004 |
| 出版者 | MATHEMATICAL SCIENCE PUBL |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59552]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Bell, Jason P. |
| 作者单位 | 1.Univ Waterloo, Dept Pure Math, Waterloo, ON, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing, Peoples R China 3.Univ Toronto Mississauga, Dept Math & Computat Sci, Mississauga, ON, Canada |
| 推荐引用方式 GB/T 7714 | Bell, Jason P.,Chen, Shaoshi,Hossain, Ehsaan. Rational dynamical systems, S-units, and D-finite power series[J]. ALGEBRA & NUMBER THEORY,2021,15(7):1699-1728. |
| APA | Bell, Jason P.,Chen, Shaoshi,&Hossain, Ehsaan.(2021).Rational dynamical systems, S-units, and D-finite power series.ALGEBRA & NUMBER THEORY,15(7),1699-1728. |
| MLA | Bell, Jason P.,et al."Rational dynamical systems, S-units, and D-finite power series".ALGEBRA & NUMBER THEORY 15.7(2021):1699-1728. |
入库方式： OAI收割
来源：数学与系统科学研究院
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